Force-balanced roller-cone bits, systems, drilling methods, and design methods

ABSTRACT

Roller cone drilling wherein the bit optimization process equalizes the downforce (axial force) for the cones (as nearly as possible, subject to other design constraints). Bit performance is significantly enhanced by equalizing downforce.

CROSS-REFERENCE TO OTHER APPLICATION

[0001] This application claims priority from U.S. provisionalapplication 60/098,466 filed Aug. 31, 1998, which is hereby incorporatedby reference.

BACKGROUND AND SUMMARY OF THE INVENTION

[0002] The present invention relates to down-hole drilling, andespecially to the optimization of drill bit parameters.

Background: Rotary Drilling

[0003] Oil wells and gas wells are drilled by a process of rotarydrilling, using a drill rig such as is shown in FIG. 10. In conventionalvertical drilling, a drill bit 10 is mounted on the end of a drillstring 12 (drill pipe plus drill collars), which may be miles long,while at the surface a rotary drive (not shown) turns the drill string,including the bit at the bottom of the hole.

[0004] Two main types of drill bits are in use, one being the rollercone bit, an example of which is seen in FIG. 11. In this bit a set ofcones 16 (two are visible) having teeth or cutting inserts 18 arearranged on rugged bearings on the arms of the bit. As the drill stringis rotated, the cones will roll on the bottom of the hole, and the teethor cutting inserts will crush the formation beneath them. (The brokenfragments of rock are swept uphole by the flow of drilling fluid.) Thesecond type of drill bit is a drag bit, having no moving parts, seen inFIG. 12.

[0005] There are various types of roller cone bits: insert-type bits,which are normally used for drilling harder formations, will have teethof tungsten carbide or some other hard material mounted on their cones.As the drill string rotates, and the cones roll along the bottom of thehole, the individual hard teeth will induce compressive failure in theformation. The bit's teeth must crush or cut rock, with the necessaryforces supplied by the “weight on bit” (WOB) which presses the bit downinto the rock, and by the torque applied at the rotary drive.

Background: Drill String Oscillation

[0006] The individual elements of a drill string appear heavy and rigid.However, in the complete drill string (which can be more than a milelong), the individual elements are quite flexible enough to allowoscillation at frequencies near the rotary speed. In fact, manydifferent modes of oscillation are possible. (A simple demonstration ofmodes of oscillation can be done by twirling a piece of rope or chain:the rope can be twirled in a flat slow circle, or, at faster speeds, sothat it appears to cross itself one or more times.) The drill string isactually a much more complex system than a hanging rope, and canoscillate in many different ways; see WAVE PROPAGATION IN PETROLEUMENGINEERING, Wilson C. Chin, (1994).

[0007] The oscillations are damped somewhat by the drilling mud, or byfriction where the drill pipe rubs against the walls, or by the energyabsorbed in fracturing the formation: but often these sources of dampingare not enough to prevent oscillation. Since these oscillations occurdown in the wellbore, they can be hard to detect, but they are generallyundesirable. Drill string oscillations change the instantaneous force onthe bit, and that means that the bit will not operate as designed. Forexample, the bit may drill oversize, or off-center, or may wear out muchsooner than expected. Oscillations are hard to predict, since differentmechanical forces can combine to produce “coupled modes”; the problemsof gyration and whirl are an example of this.

Background: Optimal Drilling with Various Formation Types

[0008] There are many factors that determine the drillability of aformation. These include, for example, compressive strength, hardnessand/or abrasiveness, elasticity, mineral content (stickiness),permeability, porosity, fluid content and interstitial pressure, andstate of underground stress.

[0009] Soft formations were originally drilled with “fish-tail” dragbits, which sheared the formation. Fish-tail bits are obsolete, butshear failure is still very useful in drilling soft formations. Rollercone bits designed for drilling soft formations are designed to maximizethe gouging and scraping action, in order to exploit both shear andcompressive failure. To accomplish this, cones are offset to induce thelargest allowable deviation from rolling on their true centers. Journalangles are small and cone-profile angles will have relatively largevariations. Teeth are long, sharp, and widely-spaced to allow for thegreatest possible penetration. Drilling in soft formations ischaracterized by low weight and high rotary speeds.

[0010] Hard formations are drilled by applying high weights on the drillbits and crushing the formation in compressive failure. The rock willfail when the applied load exceeds the strength of the rock. Roller conebits designed for drilling hard formations are designed to roll as closeas possible to a true roll, with little gouging or scrapping action.Offset will be zero and journal angles will be higher. Teeth are shortand closely spaced to prevent breakage under the high loads. Drilling inhard formations is characterized by high weight and low rotary speeds.

[0011] Medium formations are drilled by combining the features of softand hard formation bits. The rock is failed by combining compressiveforces with limited shearing and gouging action that is achieved bydesigning drill bits with a moderate amount of offset. Tooth length isdesigned for medium extensions as well. Drilling in medium formations ismost often done with weights and rotary speeds between that of the hardand soft formations.

Background: Roller Cone Bit Design

[0012] The “cones” in a roller cone bit need not be perfectly conical(nor perfectly frustroconical), but often have a slightly swollen axialprofile. Moreover, the axes of the cones do not have to intersect thecenterline of the borehole. (The angular difference is referred to asthe “offset” angle.) Another variable is the angle by which thecenterline of the bearings intersects the horizontal plane of the bottomof the hole, and this angle is known as the journal angle. Thus as thedrill bit is rotated, the cones typically do not roll true, and acertain amount of gouging and scraping takes place. The gouging andscraping action is complex in nature, and varies in magnitude anddirection depending on a number of variables.

[0013] Conventional roller cone bits can be divided into two broadcategories: Insert bits and steel-tooth bits. Steel tooth bits areutilized most gently in softer formation drilling, whereas insert bitsare utilized most frequently in medium and hard formation drilling.

[0014] Steel-tooth bits have steel teeth formed integral to the cone. (Ahard facing is typically applied to the surface of the teeth to improvethe wear resistance of the structure.) Insert bits have very hardinserts (e.g. specially selected grades of tungsten carbide) pressedinto holes drilled into the cone surfaces. The inserts extend outwardlybeyond the surface of the cones to form the “teeth” that comprise thecutting structures of the drill bit.

[0015] The design of the component elements in a rock bit areinterrelated (together with the size limitations imposed by the overalldiameter of the bit), and some of the design parameters are driven bythe intended use of the product. For example, cone angle and offset canbe modified to increase or decrease the amount of bottom hole scraping.Many other design parameters are limited in that an increase in oneparameter may necessarily result in a decrease of another. For example,increases in tooth length may cause interference with the adjacentcones.

Background: Tooth Design

[0016] The teeth of steel tooth bits are predominantly of the inverted“V” shape. The included angle (i.e. the sharpness of the tip) and thelength of the tooth will vary with the design of the bit. In bitdesigned for harder formations the teeth will be shorter and theincluded angle will be greater. Gage row teeth (i.e. the teeth in theoutermost row of the cone, next to the outer diameter of the borehole)may have a “T” shaped crest for additional wear resistance.

[0017] The most common shapes of inserts are spherical, conical, andchisel. Spherical inserts have a very small protrusion and are used fordrilling the hardest formations. Conical inserts have a greaterprotrusion and a natural resistance to breakage, and are often used fordrilling medium hard formations.

[0018] Chisel shaped inserts have opposing flats and a broad elongatedcrest, resembling the teeth of a steel tooth bit. Chisel shaped insertsare used for drilling soft to medium formations. The elongated crest ofthe chisel insert is normally oriented in alignment with the axis ofcone rotation. Thus, unlike spherical and conical inserts, the chiselinsert may be directionally oriented about its center axis. (This istrue of any tooth which is not axially symmetric.) The axial angle oforientation is measured from the plane intersecting the center of thecone and the center of the tooth.

Background: Bottom Hole Analysis

[0019] The economics of drilling a well are strongly reliant on rate ofpenetration. Since the design of the cutting structure of a drill bitcontrols the bit's ability to achieve a high rate of penetration,cutting structure design plays a significant role in the overalleconomics of drilling a well.

[0020] It has long been desirable to predict the development of bottomhole patterns on the basis of the controllable geometric parameters usedin drill bit design, and complex mathematical models can simulate bottomhole patterns to a limited extent. To accomplish this it is necessary tounderstand first, the relationship between the tooth and the rock, andsecond, the relationship between the design of the drill bit and themovement of the tooth in relation to the rock. It is also known thatthese mechanisms are interdependent.

[0021] To better understand these relationships, much work has been doneto determine the amount of rock removed by a single tooth of a drillbit. As can be seen by the forgoing discussion, this is a complexproblem. For many years it has been known that rock failure is complex,and results from the many stresses arising from the combined movementsand actions of the tooth of a rock bit. (Sikarskie, et al, PENETRATIONPROBLEMS IN ROCK MECHANICS, ASME Rock Mechanics Symposium, 1973).Subsequently, work was been done to develop quantitative relationshipsbetween bit design and tooth-formation interaction. This has beenaccomplished by calculating the vertical, radial and tangential movementof the teeth relative to the hole bottom, to accurately represent thegouging and scrapping action of the teeth on roller cone bits. (Ma, ANEW WAY TO CHARACTERIZE THE GOUGING-SCRAPPING ACTION OF ROLLER CONEBITS, Society of Petroleum Engineers No. 19448, 1989). More recently,computer programs have been developed which predict and simulate thebottom hole patterns developed by roller cone bits by combining thecomplex movement of the teeth with a model of formation failure. (Ma,THE COMPUTER SIMULATION OF THE INTERACTION BETWEEN THE ROLLER BIT ANDROCK, Society of Petroleum Engineers No. 29922, 1995). Such formationfailure models include a ductile model for removing the formationoccupied by the tooth during its movement across the bottom of the hole,and a fragile breakage model to represent the surrounding breakage.

[0022] Currently, roller cone bit designs remain the result ofgenerations of modifications made to original designs. The modificationsare based on years of experience in evaluating bit run records and dullbit conditions. Since drill bits are run under harsh conditions, farfrom view, and to destruction, it is often very difficult to determinethe cause of the failure of a bit. Roller cone bits are oftendisassembled in manufacturers' laboratories, but most often this processis in response to a customer's complaint regarding the product, when averification of the materials is required. Engineers will visit the laband attempt to perform a forensic analysis of the remains of a rock bit,but with few exceptions there is generally little evidence to supporttheir conclusions as to which component failed first and why. Since rockbits are run on different drilling rigs, in different formations, underdifferent operating conditions, it is extremely difficult drawconclusion from the dull conditions of the bits. As a result, evaluatingdull bit conditions, their cause, and determining design solutions is avery subjective process. What is known is that when the cuttingstructure or bearing system of a drill bit fails prematurely, it canhave a serious detrimental effect of the economics of drilling.

[0023] Though numerical methods are now available to model the bottomhole pattern produced by a roller cone bit, there is no suggestion as tohow this should be used to improve the design of the bits other than topredict the presence of obvious problems such as tracking. For example,the best solution available for dealing with the problems of lateralvibration, is a recommendation that roller cone bits should be run atlow to moderate rotary speeds when drilling medium to hard formations tocontrol bit vibrations and prolong life, and to use downhole vibrationsensors. (Dykstra, et al, EXPERIMENTAL EVALUATIONS OF DRILL STRINGDYNAMICS, Amoco Report Number F94-P-80, 1994).

Force-Balanced Roller-Cone Bits, Systems Drilling Methods, and DesignMethods

[0024] The present application describes improved methods for designingroller cone bits, as well as improved drilling methods, and drillingsystems. The present application teaches that roller cone bit designsshould have equal mechanical downforce on each of the cones. This is nottrivial: without special design consideration, the weight on bit willNOT automatically be equalized among the cones.

[0025] Roller-cone bits are normally NOT balanced, for several reasons:

[0026] Asymmetric cutting structures. Usually the rows on cones areintermeshed in order to cover fully the hole bottom and have aself-clearance effects. Therefore, even the cone shapes may be the samefor all three cones, the teeth row distributions on cones are differentfrom cone to cone. The number of teeth on cones are usually different.Therefore, the cone having more row and more teeth than other two conesmay remove more rock and as a results, may spent more energy (EnergyImbalance). An energy imbalance usually leads to bit force imbalance.

[0027] Offset effects. Because of the offset, a scraping motion will beinduced. This scraping motion is different from teeth row to teeth rowand as a result, the scraping force (tangent force) acting on teeth isdifferent from row to row. This will generate an imbalance force on bit.

[0028] Tracking effects. If at least one of the cones is in tracking,then this cone will gear with the hole bottom without penetration, therock not removed by this cone will be partly removed by other two cones.As a result, the bit is unbalanced.

[0029] The applicant has discovered, and has experimentally verified,that equalization of downforce per cone is a very important (and greatlyunderestimated) factor in roller cone performance. Equalized downforceis believed to be a significant factor in reducing gyration, and hasbeen demonstrated to provide substantial improvement in drillingefficiency. The present application describes bit design procedureswhich provide optimization of downforce balancing as well as otherparameters.

[0030] A roller-cone bit will always be a strong source of vibration,due to the sequential impacts of the bit teeth and the inhomogeneitiesof the formation. However, many results of this vibration areundesirable. It is believed that the improved performance ofbalanced-downforce cones is partly due to reduced vibration.

[0031] Any force imbalance at the cones corresponds to a bending torque,applied to the bottom of the drill string, which rotates with the drillstring. This rotating bending moment is a driving force, at the rotaryfrequency, which has the potential to couple to oscillations of thedrill string. Moreover, this rotating bending moment may be a factor inbiasing the drill string into a regime where vibration and instabilitiesare less heavily damped. It is believed that the improved performance ofbalanced-downforce cones may also be partly due to reduced oscillationof the drill string.

[0032] The disclosed innovations, in various embodiments, provide one ormore of at least the following advantages:

[0033] The roller cone bit is force balanced such that axial loadingbetween the arms is substantially equal.

[0034] The roller cone bit is energy balanced such that each of thecutting structures drill substantially equal volumes of formation.

[0035] The drill bit has decreased axial and lateral operatingvibration.

[0036] The cutting structures, bearings, and seals have increasedlifetime and improved performance and durability.

[0037] Drill string life is extended.

[0038] The roller cone bit has minimized tracking of cutting structures,giving improved performance and extending cutting structure life.

[0039] The roller cone bit has an optimized number of teeth in a givenformation area.

[0040] Bit performance is improved.

[0041] Off-center rotation is minimized.

[0042] The roller cone bit has optimized (minimized and equalized) uncutformation ring width.

[0043] Energy balanced roller cone bits can be further optimized byminimizing cone and bit tracking.

[0044] Energy balanced roller cone bits can be further optimized byminimizing and equalizing uncut formation rings.

[0045] Designer can evaluate the force balance and energy balanceconditions of existing bit designs.

[0046] Designer can design force balanced drill bits with predictablebottom hole patterns without relying on lab tests followed by designmodifications.

[0047] Designer can optimize the design of roller cone drill bits withindesigner-chosen constraints.

[0048] Other advantages of the various disclosed inventions will becomeapparent from the following descriptions, taken in connection with theaccompanying drawings, wherein, by way of illustration and example, asample embodiment is disclosed.

[0049] U.S. patent application Ser. No. ______, filed Aug. 31, 1999,entitled “Roller-cone Bits, Systems, Drilling Methods, and DesignMethods with Optimization of Tooth Orientation” (Atty. Docket No.SC-98-26), and claiming priority from U.S. Provisional Application60/098,442 filed Aug. 31, 1998, describes roller cone drill bit designmethods and optimizations which can be used separately from or insynergistic combination with the methods disclosed in the presentapplication. That application, which has common ownership, inventorship,and effective filing date with the present application, and itsprovisional priority application, are both hereby incorporated byreference.

BRIEF DESCRIPTION OF THE DRAWING

[0050] The disclosed inventions will be described with reference to theaccompanying drawings, which show important sample embodiments of theinvention and which are incorporated in the specification hereof byreference, wherein:

[0051]FIG. 1 shows an element and how the tooth is divided into elementsfor tooth force evaluation.

[0052]FIG. 2 diagrammatically shows a roller cone and the bearing forceswhich are measured in the current disclosure.

[0053]FIG. 3 shows the four design variables of a tooth on a cone.

[0054]FIG. 4 shows the bottom hole pattern generated by a steel toothbit.

[0055]FIG. 5 shows the layout of row distribution in a plane showing thedistance between any two tooth surfaces.

[0056]FIG. 6 shows a flowchart of the optimization procedure to design aforce balanced bit.

[0057] FIGS. 7A-C compare the three cone profiles before and afteroptimization.

[0058] FIGS. 8A-B compare the bottom hole pattern before and afteroptimization.

[0059] FIGS. 9A-B compare the cone layout before and after optimization.

[0060]FIG. 10 shows an example of a drill rig which can use bitsdesigned by the disclosed method.

[0061]FIG. 11 shows an example of a roller cone bit.

[0062]FIG. 12 shows an example of a drag bit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0063] The numerous innovative teachings of the present application willbe described with particular reference to the presently preferredembodiment (by way of example, and not of limitation).

Rock Bit Computer Model

[0064] The present invention uses a single element force-cuttingrelationship in order to develop the total force-cutting relationship ofa cone and of an entire roller cone bit. Looking at FIG. 1, each tooth,shown on the right side, can be thought of as composed of a collectionof elements, such as are shown on the left side. Each element used inthe present invention has a square cross section with area S_(e) (itscross-section on the x-y plane) and length L_(e) (along the z axis). Theforce-cutting relationship for this single element may be described by:

F _(ze) =k _(e) *σ*S _(e)  (1)

F _(xe)=μ_(x) *F _(ze)  (2)

F _(ye)=μ_(y) *F _(ze)  (3)

[0065] where F_(ze) is the normal force and F_(xe), F_(ye) are sideforces, respectively, σ is the compressive strength, S_(e) the cuttingdepth and k_(e), μ_(x) and μ_(y) are coefficient associated withformation properties. These coefficients may be determined by lab test.A tooth or an insert can always be divided into several elements.Therefore, the total force on a tooth can be obtained by integratingequation (1) to (3). The single element force model used in theinvention has significant advantage over the single tooth or singleinsert model used in most of the publications. The only way to obtain aforce model is by lab test. There are many types of inserts used todayfor roller cone bit depending on the rock type drilled. If the singleinsert force model is used, a lot of tests have to be done and this isvery difficult if not impossible. By using the element force model, onlya few tests may be enough because any kind of insert or tooth can bealways divided into elements. In other words, one element model may beapplied to all kinds of inserts or teeth.

[0066] After having the single element force model, the next step is todetermine the interaction between inserts and the formation drilled.This step involves the determination of the tooth kinematics (local)from the bit and cone kinematics (global) as described below.

[0067] (1) The bit kinematics is described by bit rotation speed, Ω=RPM(revolutions per minute), and the rate of penetration, ROP. Both RPM andROP may be considered as constant or as function with time.

[0068] (2) The cone kinematics is described by cone rotational speed.Each cone may have its own speed. The initial value is calculated fromthe bit geometric parameters or just estimated from experiment. In thecalculation the cone speed may be changed based on the torque acting onthe cone.

[0069] (3) At the initial time, t0, the hole bottom is considered as aplane and is meshed into small grids. The tooth is also meshed intogrids (single elements). At any time t, the position of a tooth in spaceis fully determined. If the tooth is in interaction with the holebottom, the hole bottom is updated and the cutting depth for eachcutting element is calculated and the forces acting on the elements areobtained.

[0070] (4) The element forces are integrated into tooth forces, thetooth forces are integrated into cone forces, the cone forces aretransferred into bearing forces and the bearing forces are integratedinto bit forces.

[0071] (5) After the bit is fully drilled into the rock, these forcesare recorded at each time step. A period time usually at least 10seconds is simulated. The average forces may be considered as staticforces and are used for evaluation of the balance condition of thecutting structure.

Evaluation of A Force Balanced Roller Cone Bit

[0072] The applied forces to bit are the weight on bit (WOB) and torqueon bit (TOB). These forces will be taken by three cones. Due to theasymmetry of bit geometry, the loads on three cones are usually notequal. In other words, one of the three cones may do much more work thanother two cones. With reference to FIG. 2, the balance condition of aroller cone bit may be evaluated using the following criteria:

Max (ω1, ω2, ω3)−Min (ω1, ω2, ω3)≦ω0  (4)

Max (η1, η2, η3)−Min (η1, η2, η3)≦η0  (5)

Max (λ1, λ2, λ3)−Max (λ1, λ2, λ3)≦λ0  (6)

ε=F _(r) /WOB*100%≦ε0  (7)

[0073] where ωi (i=1, 2, 3) is defined by ωi=WOBi/WOB*100%, WOBi is theweight on bit taken by cone i. ηi is defined by ηi =Fzi/ΣFzi*100% withFzi being the i-th cone axial force. And λi is defined by λi=Mzi/*100%with Mzi being the i-th cone moment in the direction perpendicular toi-th cone axis. Finally ε is the bit imbalance force ratio with F_(r)being the bit imbalance force. A bit is perfectly balanced if:

ω1=ω2=ω3=33.333% or ω0=0.0%

η1=η2=η3=33.333% or η0=0.0%

λ1=λ2=λ3=33.333% or λ0=0.0%

ε=0.0%

[0074] In most cases if ω0, η0, λ0, ε0 are controlled with somelimitations, the bit is balanced. The values of ω0, η0, λ0, ε0 depend onbit size and bit type.

[0075] There is a distinction between force balancing techniques andenergy balancing. A force balanced bit uses multiple objectiveoptimization technology, which considers weight on bit, axial force, andcone moment as separate optimization objectives. Energy balancing usesonly single objective optimization, as defined in equation (11) below.

Design of A Force Balanced Roller Cone Bit

[0076] As we stated in previous sections, there are many parameterswhich affect bit balance conditions. Among these parameters, the teethcrest length, their positions on cones (row distribution on cone) andthe number of teeth play a significant role. An increase in the size ofany one parameter must of necessity result in the decrease or increaseof one or more of the others. And in some cases design rules may beviolated. Obviously the development of optimization procedure isabsolutely necessary.

[0077] The first step in the optimization procedure is to choose thedesign variables. Consider a cone of a steel tooth bit as shown in FIG.3. The cone has three rows. For the sake of simplicity, the journalangle, the offset and the cone profile will be fixed and will not be asdesign variables. Therefore the only design variables for a row are thecrest length, Lc, the radial position of the center of the crest length,Rc, and the tooth angles, α and β. Therefore, the number of designvariables is 4 times of the total number of rows on a bit.

[0078] The second step in the optimization procedure is to define theobjectives and express mathematically the objectives as function ofdesign variables. According to equation (1), the force acting on anelement is proportional to the rock volume removed by that element. Thisprinciple also applies to any tooth. Therefore, the objective is to leteach cone remove the same amount of rock in one bit revolution. This iscalled volume balance or energy balance. The present inventor has foundthat an energy balanced bit will lead to force balanced in most cases.Consider FIG. 4 which shows the patterns cut by each cone on the holebottom. The first rows of all three cones have overlap and the innerrows remove the rock independently. Suppose the bit has a cutting depthΔ in one bit revolution. It is not difficult to calculate the volumesremoved by each row and the volume matrix may have the form:

V=[V _(ij)], i=1, 2, 3; j=1, 2, 3, 4,  (8)

[0079] where i represent the cone number and j the row number. Forexample, V₃₂ is the element in the volume matrix representing the rockvolume removed by the second row of the third cone. The elements V_(ij)of this matrix are all functions of the design variables.

[0080] In reality, the removed volume by each row depends not only onthe above design variables, but also on the number of teeth on that rowand the tracking condition. Therefore the volume matrix calculated in a2D manner must be scaled. The scale matrix, K_(v), may be obtained asfollows.

K _(v)(i,j)=V _(3d0)(i,j)/V _(2d0)(i,j)  (9)

[0081] where V_(3d0) is the volume matrix of the initial designed bit(before optimization). V_(3d0) is obtained from the rock bit computerprogram by simulate the bit drilling procedure at least 10 seconds.V_(2d0) is the volume matrix associated with the initial designed matrixand obtained using the 2D manner based on the bottom pattern shown inFIG. 4. The volume matrix has the final form:

V _(b)(i,j)=K _(v)(i,j)*V(i,j)=f _(v)(L _(c) , R _(c), α,β)  (10)

[0082] Let V₁, V₂ and V₃ be the volume removed by cone 1, 2 and 3,respectively. For the energy balance, the objective function takes thefollowing form:

Obj=(V ₁ −V _(m))^ 2+(V ₂ −V _(m))^ 2+(V ₃ −V _(m))^ 2  (11)

[0083] where V_(m)=(V₁+V₂+V₃)/3;

[0084] The third step in the optimization procedure is to define thebounds of the design variables and the constraints. The lower and upperbounds of design variables can be determined by requirements on elementstrength and structural limitation. For example, the lower bound of atooth crest length is determined by the tooth strength. The angle α andβ may be limited to 0˜45 degrees. One of the most important constraintsis the interference between teeth on different cones. A minimumclearance between teeth surface must be kept. Consider FIG. 5 where coneprofile is shown in a plane. A minimum clearance between tooth surfacesis required. This clearance can be expressed as a function of the designvariables.

Δd=f_(d)(L_(c), R_(c), α, β)  (12)

[0085] Another constraint is the width of the uncut formation rings onbottom. The width of the uncut formation rings should be minimized orequalized in order to avoid the direct contact of cone surface toformation drilled. These constraints can be expressed as:

Δw_(min)≦≢wi=fw_(i)(L_(c), R_(c), α, β)≦Δw_(max)  (13)

[0086] There may be other constraints, for example, the minimum spacebetween two neighbored rows on the same cone required by the miningprocess.

[0087] After having the objective function, the bounds and theconstraints, the problem is simplified to a general nonlinearoptimization problem with bounds and nonlinear constrains which can besolved by different methods. FIG. 6 shows the flowchart of theoptimization procedure. The procedure begins by reading the bit geometryand other operational parameters. The forces on the teethe cones,bearings, and bit are then calculated. Once the forces are known, theyare compared, and if they are balanced, then the design is optimized. Ifthe forces are not balanced, then the optimization must occur.Objectives, constraints, design variables and their bounds (maximum andminimum allowed values) are defined, and the variables are altered toconform to the new objectives. Once the new objectives are met, the newgeometric parameters are used to re-design the bit, and the forces areagain calculated and checked for balance. This process is repeated untilthe desired force balance is achieved.

[0088] As an example, FIGS. 7A-C show the row distributions on threecones of a 9″ steel tooth bit before and after optimization. FIGS. 8Aand 8B compare the bottom hole patterns cut by the different conesbefore and after optimization. FIGS. 9A and B compare the cone layoutsbefore and after optimization.

[0089] In the preferred embodiment of the present disclosure, a rollercone bit is provided for which the volume of formation removed by eachtooth in each row, of each cutting structure (cone), is calculated. Thiscalculation is based on input data of bit geometry, rock properties, andoperational parameters. The geometric parameters of the roller cone bitare then modified such that the volume of formation removed by eachcutting structure is equalized. Since the amount of formation removed byany tooth on a cutting structure is a function of the force imparted onthe formation by the tooth, the volume of formation removed by a cuttingstructure is a direct function of the force applied to the cuttingstructure. By balancing the volume of formation removed by all cuttingstructures, force balancing is also achieved.

[0090] As another feature of the preferred embodiment, a roller cone bitis provided for which the width of the rings of formation remaininguncut is calculated, as it remains between the rows of the intermeshingteeth of the different cutting structures. The geometric parameters ofthe roller cone bit are then modified such that the width of the uncutarea for each row is substantially minimized and equalized withinselected acceptable limits. By minimizing the uncut rings on the bottomof the hole, the bit will be able to crush the uncut ring uponsuccessive rotations due to the craters of formation removed immediatelyadjacent to the uncut rings. By equalizing the width of the uncut rings,the force required to crush the rings will be even from any point on thehole face, such that as cutting elements (teeth) engage the rings onsuccessive rotations, the rings act to uniformly retain the bit drillingon-center.

[0091] According to a disclosed class of innovative embodiments, thereis provided: A roller cone drill bit comprising: a plurality of arms;rotatable cutting structures mounted on respective ones of said arms;and a plurality of teeth located on each of said cutting structures;wherein approximately the same axial force is acting on each of saidcutting structure.

[0092] According to another disclosed class of innovative embodiments,there is provided: A roller cone drill bit comprising: a plurality ofarms; rotatable cutting structures mounted on respective ones of saidarms; and a plurality of teeth located on each of said cuttingstructures; wherein a substantially equal volume of formation is drilledby each said cutting structure.

[0093] According to another disclosed class of innovative embodiments,there is provided: A rotary drilling system, comprising: a drill stingwhich is connected to conduct drilling fluid from a surface location toa rotary drill bit; a rotary drive which rotates at least part of saiddrill string together with said bit said rotary drill bit comprising aplurality of arms; rotatable cutting structures mounted on respectiveones of said arms; and a plurality of teeth located on each of saidcutting structures; wherein approximately the same axial force is actingon each said cutting structure.

[0094] According to another disclosed class of innovative embodiments,there is provided: A method of designing a roller cone drill bit,comprising the steps of: (a) calculating the volume of formation cut byeach tooth on each cutting structure; (b) calculating the volume offormation cut by each cutting structure per revolution of the drill bit;(c) comparing the volume of formation cut by each of said cuttingstructures with the volume of formation cut by all others of saidcutting structure of the bit; (d) adjusting at least one geometricparameter on the design of at least one cutting structure; and (e)repeating steps (a) through (d) until substantially the same volume offormation is cut by each of said cutting structures of said bit.

[0095] According to another disclosed class of innovative embodiments,there is provided: A method of designing a roller cone drill bit; thesteps of comprising: (a) calculating the axial force acting on eachtooth on each cutting structure; (b) calculating the axial force actingon each cutting structure per revolution of the drill bit; (c) comparingthe axial force acting on each of said cutting structures with the axialforce on the other ones of said cutting structures of the bit; (d)adding at least one geometric parameter on the design of at least onecutting structure; (e) repeating steps (a) through (d) untilapproximately the same axial force is acting on each cutting structure.

[0096] According to another disclosed class of innovative embodimentthere is provided: A method of designing a roller cone drill bit, thesteps of comprising: (a) calculating the force balance conditions of abit; (b) defining design variables; (c) determine lower and upper boundsfor the design variables; (d) defining objective functions, (e) definingconstraint functions; (f) performing an optimization means; and, (g)evaluating an optimized cutting structure by modeling.

[0097] According to another disclosed class of innovative embodiments,there is provided: A method of using a roller cone drill bit; comprisingthe step of rotating said roller cone drill bit such that substantiallythe same volume of formation is cut by each roller cone of said bit.

[0098] According to another disclosed class of innovative embodiments,there is provided: A method of using a roller cone drill bit, comprisingthe step of said roller cone drill bit such that substantially the sameaxial force is acting on each roller cone of said bit.

Modifications and Variations

[0099] As will be recognized by those skilled in the art, the innovativeconcepts described in the present application can be modified and variedover a tremendous range of applications, and accordingly the scope ofpatented subject matter is not limited by any of the specific exemplaryteachings given.

[0100] Additional general background, which helps to show the knowledgeof those skilled in the art regarding implementations and thepredictability of variations, may be found in the followingpublications, all of which are hereby incorporated by reference: APPLIEDDRILLING ENGINEERING, Adam T. Bourgoyne Jr. et al., Society of PetroleumEngineers Textbook series (1991), OIL AND GAS FIELD DEVELOPMENTTECHNIQUES: DRILLING, J.-P. Nguyen (translation 1996, from Frenchoriginal 1993), MAKING HOLE (1983) and DRILLING MUD (1984), both part ofthe Rotary Drilling Series, edited by Charles Kirkley.

[0101] None of the description in the present application should be readas implying that any particular element, step, or function is anessential element which must be included in the claim scope: THE SCOPEOF PATENTED SUBJECT MATTER IS DEFINED ONLY BY THE ALLOWED CLAIMS.Moreover, none of these claims are intended to invoke paragraph six of35 USC section 112 unless the exact words “means for” are followed by aparticiple.

What is claimed is:
 1. A roller cone drill bit comprising: a pluralityof arms; rotatable cutting structures mounted on respective ones of saidarms; and a plurality of teeth located on each of said cuttingstructures; wherein approximately the same axial force is acting on eachof said cutting structure.
 2. The roller cone drill bit of claim 1 ,wherein the axial force on each of said cutting structure is betweenthirty-one (31) percent and thirty-five (35) percent of the total of theaxial force on the bit.
 3. A roller cone drill bit comprising: aplurality of arms; rotatable cutting structures mounted on respectiveones of said arms; and a plurality of teeth located on each of saidcutting structures; wherein a substantially equal volume of formation isdrilled by each said cutting structure.
 4. The roller cone drill bit ofclaim 3 , wherein the volume of formation drilled by each of saidcutting structures is between thirty-one (31) percent and thirty-five(35) percent of the total volume drilled by the drill bit.
 5. A rotarydrilling system, comprising: a drill string which is connected toconduct drilling fluid from a surface location to a rotary drill bit; arotary drive which rotates at least part of said drill string togetherwith said bit said rotary drill bit comprising a plurality of arms;rotatable cutting structures mounted on respective ones of said arms;and a plurality of teeth located on each of said cutting structure;wherein approximately the same axial force is acting on each of saidcutting structure.
 6. A method of designing a roller cone drill bit,comprising the steps of: (a) calculating the volume of formation cut byeach tooth on each cutting structure; (b) calculating the volume offormation cut by a cutting structure per revolution of the drill bit;(c) comparing the volume of formation cut by each of a cuttingstructures with the volume of formation cut by all others of saidcutting structures of the bit; (d) adjusting at least one geometricparameter on the design of at least one cutting structure; and (e)repeating steps (a) through (d) until substantially the same volume offormation is cut by each of said cutting structures of said bit.
 7. Themethod of claim 6 , wherein the step of calculating the volume offormation cut by each tooth on each cutting structure further comprisesthe step of using numerical simulation to determine the intervalprogression of each tooth as it intersects the formation.
 8. A method ofdesigning a roller cone drill bit, the steps of comprising: (a)calculating the axial force acting on each tooth on each cuttingstructure; (b) calculating the axial force acting on each cuttingstructure per revolution of the drill bit; (c) comparing the axial forceacting on each of said cutting structures with the axial force on theother ones of said cutting structures of the bit; (d) adjusting at leastone geometric parameter on the design of at least one cutting structure;(e) repeating steps (a) through (d) until approximately the same axialforce is acting on each cutting structure.
 9. The method of claim 8 ,wherein the step of calculating the normal force acting on each tooth,on each cutting structure further comprises the step of using numericalsimulation to determine the interval progression of each tooth as itintersects the formation.
 10. The method of claim 8 , further comprisingthe steps of (a) calculating the volume of formation displaced by thedepth of penetration of each tooth; (b) calculating the volume offormation displaced by the tangential scrapping movement of each tooth;(c) calculating the volume of formation displaced by the radialscrapping movement of each tooth; and, (d) calculating the volume offormation displaced by a crater enlargement parameter function.
 11. Amethod of designing a roller cone drill bit, the steps of comprising:(a) calculating the force balance conditions of a bit; (b) definingdesign variables; (c) determine lower and upper bounds for the designvariable (d) defining objective functions; (e) defining constrainfunctions; (f) performing an optimization means; and, (g) evaluating anoptimized cutting structure by modeling.
 12. A method of using a rollercone drill bit, comprising the step of rotating said roller cone drillbit such that substantially the same volume of formation is cut by eachroller cone of said bit.
 13. A method of using a roller cone drill bit,comprising the step of rotating said roller cone drill bit such thatsubstantially the same axial form is acting on each roller cone of saidbit.